{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

STAT1301 T10 Solution

# STAT1301 T10 Solution - THE UNIVERSITY OF HONG KONG...

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT1301 PROBABILITY AND STATISTICS I EXAMPLE CLASS 10 EX.1 Let X and Y be random variables with joint pdf my, if0<zv<y<oo f(:c,y)={ y 0, otherwise Let W=Y~X, Z=Y+X. Find thejoint pdfofT/V and Z. uz7~x,%=7+>< ; “2’-” “fig 0 Z ,— C) X”:— , T, L {fa/L5wa J H) JIYIXﬁ): %% .:/’7”l§ iii/:11 %%~%§g : Z Z _ {2%) 2%)8 ﬁx”): 1:5):- {31/ 2.. — wig—U— EX.2 Suppose X and Y have joint density function ﬂay) ={ (a) Find the joint density function of U :z X Y and V = X / Y. (b) Find the marginal pde of U and V. I 1 \$2712 7 0, ﬁm>Ly>1 otherwise A) U=X7’ , VL—é ® X=ﬁ/7, 7:]; (XM 7 mix )2 posiﬁdd) Hence, 1% “bu/(WM 25 l—l. ﬂ 2.9: as [K EA. Joey)?“ 3" am 2” 2—4-1.-1 g2 % gin *M 41/ ¥V«.2V 6U -& 3W 6% jam « « M‘FéZ/MM 1/0qu by i 7, -1: -.__l__\ I 7A,[email protected]) bu/M 2V/“2m/ ) ZiSI/SM,/ ,U‘f 1’) Muﬁiﬁmw : J L‘ 2w[/&VJ—Lg .. ﬁx 7 / KM<°° ﬁSng‘ é?) MamﬂxGé/V) 5r 0<V<( , - “Q! i I Id», _ 10”" 527174“ 2:7 72' .L ~ 2/ V ’m, s< 6 41/“) 064,61 ,.L -1“:J. V”): Law “21/ M r 2% EX.3 Suppose X, Y and Z are independently and identically distributed as E\$p(1). Derive the joint distribution of U 2 X + Y, V = X + Z and W = Y + Z. ﬂag“ MM% King a 10020253): 57‘ 9'1 52 : €~c9aﬂfj I 27aykaz70 U= X”, W X+g , N: we A k ( Q7 )<- Emma) / rid/mm) , %=:’(V+N~U) Hem ?f Z5 A H mﬂmﬁm BJA 9M 9a ( I Jzatx-é-Bﬁ O" 9Kﬂav2(0(:‘l 9x395? engage 9’{ exaggﬁ [AL govt We (6 U, mu :; 5c"ij -1 “.1 stud/IN) : 6 20/06 VfLﬂ/KJ/ : 204+W“)/[w/0J<Mﬂ/, 1/20,“),0 L ,4; 7670 I WWW?) .u<mV C 370 é/[l/th/‘ng @{LwV—M <1? W~VI<H<WVJ VfLH/QD N ? WV \ EX.4 __ . Suppose X, Y 1131 U(0,1). Find the pdf of Z = X + Y. 7;; dbfrlbaﬁm {‘M/(Cﬂznoﬁ :Z (’5 diam @L 6%) 2mg): P(X+“rga~/ MW Oézq, g Hf ﬂu“ 5595/» fa {(193)5ng : £%[9%’7(( K jﬁf 2. UM ./<Tzs2, _ m“ @592 ff my)an K1275; Z flforﬂmﬂédﬂ‘ r W MW 14/??? W 3 (7:4) 7‘ [w’gjéﬂ > 2%~§ /( 6/1 H ca 1 O r K?) GWZXEE , osau 2%”354 r [<2—i2 { r %}l 7W 12 p665 [3 {W by ' :6 , 0S£<f 4 {4?}: {25% r ( (E52 v > ' mag, ...
View Full Document

{[ snackBarMessage ]}

### Page1 / 4

STAT1301 T10 Solution - THE UNIVERSITY OF HONG KONG...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online